Description Usage Arguments Details Value Author(s) See Also Examples
This function helps to construct a formula
object that
can be used in a call to hhh4
to model
seasonal variation via a sum of sine and cosine terms.
1 | addSeason2formula(f = ~1, S = 1, period = 52, timevar = "t")
|
f |
formula that the seasonal terms should be added to,
defaults to an intercept |
S |
number of sine and cosine terms. If |
period |
period of the season, defaults to 52 for weekly data. |
timevar |
the time variable in the model. Defaults to |
The function adds the seasonal terms
sum_s gamma_s * sin(2*pi*s/period * t) + delta_s * cos(2*pi*s/period * t),
where gamma_s and delta_s are the unknown
parameters and t, t = 1, 2, … denotes the time
variable timevar
, to an existing formula f
.
Note that the seasonal terms can also be expressed as
γ_s sin(2*pi*s/period * t) + δ_s cos2*pi*s/period * t) = A_s sin(2*pi*s/period * t + ε_s)
with amplitude A_s=sqrt{γ_s^2 +δ_s^2} and phase difference \tan(ε_s) = δ_s / γ_s.
Returns a formula
with the seasonal terms added and
its environment set to .GlobalEnv
.
Note that to use the resulting formula in hhh4
,
a time variable named as specified by the argument timevar
must
be available.
M. Paul, with contributions by S. Meyer
1 2 3 4 5 6 7 8 | # add 2 sine/cosine terms to a model with intercept and linear trend
addSeason2formula(f = ~ 1 + t, S = 2)
# the same for monthly data
addSeason2formula(f = ~ 1 + t, S = 2, period = 12)
# different number of seasons for a bivariate time series
addSeason2formula(f = ~ 1, S = c(3, 1), period = 52)
|
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